A qualitative mathematical model of the immune response under the effect of stress

TL;DR

This paper presents a qualitative mathematical model that captures how stress influences immune response dynamics, revealing stable, oscillatory, and burnout states through bifurcation analysis.

Contribution

It introduces a simple differential equation model integrating stress effects into immune response, highlighting different health states and transitions.

Findings

Stable healthy state at low stress

Oscillatory immune response at high stress

Burn-out state at extreme stress

Abstract

In the last decades, the interest to understand the connection between brain and body has grown notably. For example, in psychoneuroimmunology many studies associate stress, arising from many different sources and situations, to changes in the immune system from the medical or immunological point of view as well as from the biochemical one. In this paper we identify important behaviours of this interplay between the immune system and stress from medical studies and seek to represent them qualitatively in a paradigmatic, yet simple, mathematical model. To that end we develop a differential equation model with two equations for infection level and immune system, which integrates the effects of stress as an additional parameter. We are able to reproduce a stable healthy state for little stress, an oscillatory state between healthy and infected states for high stress, and a "burn-out" or stable sick state for extremely high stress. The mechanism between the different dynamics is controlled by two saddle-node in cycle (SNIC) bifurcations. Furthermore, our model is able to capture an induced infection upon dropping from moderate to low stress, and it predicts increasing infection periods upon increasing before eventually reaching a burn-out state.